Solving for Y: Finding the Value of a Function’s Ordered Pair
In mathematics, a function is a relation between two sets in which each element of the first set is paired with exactly one element of the second set. The set of all input values (x-values) of a function is called the domain, while the set of all output values (y-values) is called the range. To find the value of a function’s ordered pair, we need to solve for y.
To solve for y, we need to substitute the given x-value into the function equation and simplify the expression until we get a single value for y. For example, if we have the equation y = 2x + 3 and want to find the ordered pair for x = 4, we would substitute 4 for x as follows:
y = 2(4) + 3
y = 8 + 3
y = 11
Therefore, the ordered pair (4, 11) is the solution to the equation y = 2x + 3 when x = 4.
It is important to note that functions can have multiple ordered pairs for different values of x, but each ordered pair has a unique y-value. This means that no two ordered pairs can have the same x-value and different y-values or vice versa.
In conclusion, solving for y involves substituting the given x-value into the function equation, simplifying the expression, and finding the single value for y. By doing so, we can find the value of a function’s ordered pair and understand its relationship between the input and output values.